Problem 0: Complete the Canvas quiz "PSet 2 - Canvas".

Problem (10 points): Determine if the following argument form is valid or invalid . Show your work.

$p \vee q \vee r$
$\neg p$
$q \rightarrow r$
$\therefore r$

Problem (8 points): Show how to come to the conclusion $v$ given the following premises. Show which rule of inference you used at each step and which premises and/or previous conclusions you applied them to.

$p \vee \neg q \vee r$
$p \rightarrow s$
$s \rightarrow v$
$\neg q \rightarrow \neg u$
$u$
$r \rightarrow v$

Problem (8 points): You meet four people on the Island of Knights and Knaves. Given the following statements they make, determine for each individual whether they are a knight or a knave. Show your reasoning. (Consider each utterance as a single (possibly compound) statement. Knights' statements are always true and knaves' statements are always false. )

Problem (10 points): Let $P$ be the set of players, $T$ be the set of professional teams, and $C$ be the set of college teams. Let $M(x,y)$ be the predicate "player $x$ plays for pro team $y$" and $N(x,y)$ be the predicate "player $x$ played for college team $y$".

Write each of the following in predicate logic. Be sure to indicate the domain of each quantified variable using $P$, $T$, or $C$. Assume that the specific nouns mentioned are members of the appropriate sets.